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<div class="subTitle">org.apache.commons.math3.linear</div>
<h2 title="Class MatrixUtils" class="title">Class MatrixUtils</h2>
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<pre>public class <span class="strong">MatrixUtils</span>
extends <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></pre>
<div class="block">A collection of static methods that operate on or return matrices.</div>
<dl><dt><span class="strong">Version:</span></dt>
  <dd>$Id: MatrixUtils.java 1533638 2013-10-18 21:19:18Z tn $</dd></dl>
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<h3>Field Summary</h3>
<table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Field Summary table, listing fields, and an explanation">
<caption><span>Fields</span><span class="tabEnd">&nbsp;</span></caption>
<tr>
<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Field and Description</th>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/linear/RealMatrixFormat.html" title="class in org.apache.commons.math3.linear">RealMatrixFormat</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#DEFAULT_FORMAT">DEFAULT_FORMAT</a></strong></code>
<div class="block">The default format for <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a> objects.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/linear/RealMatrixFormat.html" title="class in org.apache.commons.math3.linear">RealMatrixFormat</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#OCTAVE_FORMAT">OCTAVE_FORMAT</a></strong></code>
<div class="block">A format for <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a> objects compatible with octave.</div>
</td>
</tr>
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<h3>Method Summary</h3>
<table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Method Summary table, listing methods, and an explanation">
<caption><span>Methods</span><span class="tabEnd">&nbsp;</span></caption>
<tr>
<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Method and Description</th>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/linear/Array2DRowRealMatrix.html" title="class in org.apache.commons.math3.linear">Array2DRowRealMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#bigFractionMatrixToRealMatrix(org.apache.commons.math3.linear.FieldMatrix)">bigFractionMatrixToRealMatrix</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</a>&lt;<a href="../../../../../org/apache/commons/math3/fraction/BigFraction.html" title="class in org.apache.commons.math3.fraction">BigFraction</a>&gt;&nbsp;m)</code>
<div class="block">Convert a <a href="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear"><code>FieldMatrix</code></a>/<a href="../../../../../org/apache/commons/math3/fraction/BigFraction.html" title="class in org.apache.commons.math3.fraction"><code>BigFraction</code></a> matrix to a <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a>.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#blockInverse(org.apache.commons.math3.linear.RealMatrix, int)">blockInverse</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;m,
            int&nbsp;splitIndex)</code>
<div class="block">Computes the inverse of the given matrix by splitting it into
 4 sub-matrices.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static void</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#checkAdditionCompatible(org.apache.commons.math3.linear.AnyMatrix, org.apache.commons.math3.linear.AnyMatrix)">checkAdditionCompatible</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</a>&nbsp;left,
                       <a href="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</a>&nbsp;right)</code>
<div class="block">Check if matrices are addition compatible.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static void</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#checkColumnIndex(org.apache.commons.math3.linear.AnyMatrix, int)">checkColumnIndex</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</a>&nbsp;m,
                int&nbsp;column)</code>
<div class="block">Check if a column index is valid.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static void</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#checkMatrixIndex(org.apache.commons.math3.linear.AnyMatrix, int, int)">checkMatrixIndex</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</a>&nbsp;m,
                int&nbsp;row,
                int&nbsp;column)</code>
<div class="block">Check if matrix indices are valid.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static void</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#checkMultiplicationCompatible(org.apache.commons.math3.linear.AnyMatrix, org.apache.commons.math3.linear.AnyMatrix)">checkMultiplicationCompatible</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</a>&nbsp;left,
                             <a href="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</a>&nbsp;right)</code>
<div class="block">Check if matrices are multiplication compatible</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static void</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#checkRowIndex(org.apache.commons.math3.linear.AnyMatrix, int)">checkRowIndex</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</a>&nbsp;m,
             int&nbsp;row)</code>
<div class="block">Check if a row index is valid.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static void</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#checkSubMatrixIndex(org.apache.commons.math3.linear.AnyMatrix, int[], int[])">checkSubMatrixIndex</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</a>&nbsp;m,
                   int[]&nbsp;selectedRows,
                   int[]&nbsp;selectedColumns)</code>
<div class="block">Check if submatrix ranges indices are valid.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static void</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#checkSubMatrixIndex(org.apache.commons.math3.linear.AnyMatrix, int, int, int, int)">checkSubMatrixIndex</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</a>&nbsp;m,
                   int&nbsp;startRow,
                   int&nbsp;endRow,
                   int&nbsp;startColumn,
                   int&nbsp;endColumn)</code>
<div class="block">Check if submatrix ranges indices are valid.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static void</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#checkSubtractionCompatible(org.apache.commons.math3.linear.AnyMatrix, org.apache.commons.math3.linear.AnyMatrix)">checkSubtractionCompatible</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</a>&nbsp;left,
                          <a href="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</a>&nbsp;right)</code>
<div class="block">Check if matrices are subtraction compatible</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static void</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#checkSymmetric(org.apache.commons.math3.linear.RealMatrix, double)">checkSymmetric</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;matrix,
              double&nbsp;eps)</code>
<div class="block">Checks whether a matrix is symmetric.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static &lt;T extends <a href="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</a>&lt;T&gt;&gt;&nbsp;<br><a href="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</a>&lt;T&gt;</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createColumnFieldMatrix(T[])">createColumnFieldMatrix</a></strong>(T[]&nbsp;columnData)</code>
<div class="block">Creates a column <a href="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear"><code>FieldMatrix</code></a> using the data from the input
 array.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createColumnRealMatrix(double[])">createColumnRealMatrix</a></strong>(double[]&nbsp;columnData)</code>
<div class="block">Creates a column <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a> using the data from the input
 array.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static &lt;T extends <a href="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</a>&lt;T&gt;&gt;&nbsp;<br><a href="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</a>&lt;T&gt;</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createFieldDiagonalMatrix(T[])">createFieldDiagonalMatrix</a></strong>(T[]&nbsp;diagonal)</code>
<div class="block">Returns a diagonal matrix with specified elements.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static &lt;T extends <a href="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</a>&lt;T&gt;&gt;&nbsp;<br><a href="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</a>&lt;T&gt;</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createFieldIdentityMatrix(org.apache.commons.math3.Field, int)">createFieldIdentityMatrix</a></strong>(<a href="../../../../../org/apache/commons/math3/Field.html" title="interface in org.apache.commons.math3">Field</a>&lt;T&gt;&nbsp;field,
                         int&nbsp;dimension)</code>
<div class="block">Returns <code>dimension x dimension</code> identity matrix.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static &lt;T extends <a href="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</a>&lt;T&gt;&gt;&nbsp;<br><a href="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</a>&lt;T&gt;</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createFieldMatrix(org.apache.commons.math3.Field, int, int)">createFieldMatrix</a></strong>(<a href="../../../../../org/apache/commons/math3/Field.html" title="interface in org.apache.commons.math3">Field</a>&lt;T&gt;&nbsp;field,
                 int&nbsp;rows,
                 int&nbsp;columns)</code>
<div class="block">Returns a <a href="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear"><code>FieldMatrix</code></a> with specified dimensions.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static &lt;T extends <a href="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</a>&lt;T&gt;&gt;&nbsp;<br><a href="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</a>&lt;T&gt;</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createFieldMatrix(T[][])">createFieldMatrix</a></strong>(T[][]&nbsp;data)</code>
<div class="block">Returns a <a href="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear"><code>FieldMatrix</code></a> whose entries are the the values in the
 the input array.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static &lt;T extends <a href="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</a>&lt;T&gt;&gt;&nbsp;<br><a href="../../../../../org/apache/commons/math3/linear/FieldVector.html" title="interface in org.apache.commons.math3.linear">FieldVector</a>&lt;T&gt;</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createFieldVector(T[])">createFieldVector</a></strong>(T[]&nbsp;data)</code>
<div class="block">Creates a <a href="../../../../../org/apache/commons/math3/linear/FieldVector.html" title="interface in org.apache.commons.math3.linear"><code>FieldVector</code></a> using the data from the input array.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createRealDiagonalMatrix(double[])">createRealDiagonalMatrix</a></strong>(double[]&nbsp;diagonal)</code>
<div class="block">Returns a diagonal matrix with specified elements.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createRealIdentityMatrix(int)">createRealIdentityMatrix</a></strong>(int&nbsp;dimension)</code>
<div class="block">Returns <code>dimension x dimension</code> identity matrix.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createRealMatrix(double[][])">createRealMatrix</a></strong>(double[][]&nbsp;data)</code>
<div class="block">Returns a <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a> whose entries are the the values in the
 the input array.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createRealMatrix(int, int)">createRealMatrix</a></strong>(int&nbsp;rows,
                int&nbsp;columns)</code>
<div class="block">Returns a <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a> with specified dimensions.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createRealVector(double[])">createRealVector</a></strong>(double[]&nbsp;data)</code>
<div class="block">Creates a <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear"><code>RealVector</code></a> using the data from the input array.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static &lt;T extends <a href="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</a>&lt;T&gt;&gt;&nbsp;<br><a href="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</a>&lt;T&gt;</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createRowFieldMatrix(T[])">createRowFieldMatrix</a></strong>(T[]&nbsp;rowData)</code>
<div class="block">Create a row <a href="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear"><code>FieldMatrix</code></a> using the data from the input
 array.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createRowRealMatrix(double[])">createRowRealMatrix</a></strong>(double[]&nbsp;rowData)</code>
<div class="block">Create a row <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a> using the data from the input
 array.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static void</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#deserializeRealMatrix(java.lang.Object, java.lang.String, java.io.ObjectInputStream)">deserializeRealMatrix</a></strong>(<a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a>&nbsp;instance,
                     <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</a>&nbsp;fieldName,
                     <a href="http://docs.oracle.com/javase/6/docs/api/java/io/ObjectInputStream.html?is-external=true" title="class or interface in java.io">ObjectInputStream</a>&nbsp;ois)</code>
<div class="block">Deserialize  a <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a> field in a class.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static void</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#deserializeRealVector(java.lang.Object, java.lang.String, java.io.ObjectInputStream)">deserializeRealVector</a></strong>(<a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a>&nbsp;instance,
                     <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</a>&nbsp;fieldName,
                     <a href="http://docs.oracle.com/javase/6/docs/api/java/io/ObjectInputStream.html?is-external=true" title="class or interface in java.io">ObjectInputStream</a>&nbsp;ois)</code>
<div class="block">Deserialize  a <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear"><code>RealVector</code></a> field in a class.</div>
</td>
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<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/linear/Array2DRowRealMatrix.html" title="class in org.apache.commons.math3.linear">Array2DRowRealMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#fractionMatrixToRealMatrix(org.apache.commons.math3.linear.FieldMatrix)">fractionMatrixToRealMatrix</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</a>&lt;<a href="../../../../../org/apache/commons/math3/fraction/Fraction.html" title="class in org.apache.commons.math3.fraction">Fraction</a>&gt;&nbsp;m)</code>
<div class="block">Convert a <a href="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear"><code>FieldMatrix</code></a>/<a href="../../../../../org/apache/commons/math3/fraction/Fraction.html" title="class in org.apache.commons.math3.fraction"><code>Fraction</code></a> matrix to a <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a>.</div>
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<tr class="altColor">
<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#inverse(org.apache.commons.math3.linear.RealMatrix)">inverse</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;matrix)</code>
<div class="block">Computes the inverse of the given matrix.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#inverse(org.apache.commons.math3.linear.RealMatrix, double)">inverse</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;matrix,
       double&nbsp;threshold)</code>
<div class="block">Computes the inverse of the given matrix.</div>
</td>
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<tr class="altColor">
<td class="colFirst"><code>static boolean</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#isSymmetric(org.apache.commons.math3.linear.RealMatrix, double)">isSymmetric</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;matrix,
           double&nbsp;eps)</code>
<div class="block">Checks whether a matrix is symmetric.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static void</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#serializeRealMatrix(org.apache.commons.math3.linear.RealMatrix, java.io.ObjectOutputStream)">serializeRealMatrix</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;matrix,
                   <a href="http://docs.oracle.com/javase/6/docs/api/java/io/ObjectOutputStream.html?is-external=true" title="class or interface in java.io">ObjectOutputStream</a>&nbsp;oos)</code>
<div class="block">Serialize a <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a>.</div>
</td>
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<tr class="altColor">
<td class="colFirst"><code>static void</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#serializeRealVector(org.apache.commons.math3.linear.RealVector, java.io.ObjectOutputStream)">serializeRealVector</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a>&nbsp;vector,
                   <a href="http://docs.oracle.com/javase/6/docs/api/java/io/ObjectOutputStream.html?is-external=true" title="class or interface in java.io">ObjectOutputStream</a>&nbsp;oos)</code>
<div class="block">Serialize a <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear"><code>RealVector</code></a>.</div>
</td>
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<tr class="rowColor">
<td class="colFirst"><code>static void</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#solveLowerTriangularSystem(org.apache.commons.math3.linear.RealMatrix, org.apache.commons.math3.linear.RealVector)">solveLowerTriangularSystem</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;rm,
                          <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a>&nbsp;b)</code>
<div class="block">Solve  a  system of composed of a Lower Triangular Matrix
 <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a>.</div>
</td>
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<tr class="altColor">
<td class="colFirst"><code>static void</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#solveUpperTriangularSystem(org.apache.commons.math3.linear.RealMatrix, org.apache.commons.math3.linear.RealVector)">solveUpperTriangularSystem</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;rm,
                          <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a>&nbsp;b)</code>
<div class="block">Solver a  system composed  of an Upper Triangular Matrix
 <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a>.</div>
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<code><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</a></code></li>
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<pre>public static final&nbsp;<a href="../../../../../org/apache/commons/math3/linear/RealMatrixFormat.html" title="class in org.apache.commons.math3.linear">RealMatrixFormat</a> DEFAULT_FORMAT</pre>
<div class="block">The default format for <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a> objects.</div>
<dl><dt><span class="strong">Since:</span></dt>
  <dd>3.1</dd></dl>
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<pre>public static final&nbsp;<a href="../../../../../org/apache/commons/math3/linear/RealMatrixFormat.html" title="class in org.apache.commons.math3.linear">RealMatrixFormat</a> OCTAVE_FORMAT</pre>
<div class="block">A format for <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a> objects compatible with octave.</div>
<dl><dt><span class="strong">Since:</span></dt>
  <dd>3.1</dd></dl>
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<pre>public static&nbsp;<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;createRealMatrix(int&nbsp;rows,
                          int&nbsp;columns)</pre>
<div class="block">Returns a <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a> with specified dimensions.
 <p>The type of matrix returned depends on the dimension. Below
 2<sup>12</sup> elements (i.e. 4096 elements or 64&times;64 for a
 square matrix) which can be stored in a 32kB array, a <a href="../../../../../org/apache/commons/math3/linear/Array2DRowRealMatrix.html" title="class in org.apache.commons.math3.linear"><code>Array2DRowRealMatrix</code></a> instance is built. Above this threshold a <a href="../../../../../org/apache/commons/math3/linear/BlockRealMatrix.html" title="class in org.apache.commons.math3.linear"><code>BlockRealMatrix</code></a> instance is built.</p>
 <p>The matrix elements are all set to 0.0.</p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>rows</code> - number of rows of the matrix</dd><dd><code>columns</code> - number of columns of the matrix</dd>
<dt><span class="strong">Returns:</span></dt><dd>RealMatrix with specified dimensions</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createRealMatrix(double[][])"><code>createRealMatrix(double[][])</code></a></dd></dl>
</li>
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<h4>createFieldMatrix</h4>
<pre>public static&nbsp;&lt;T extends <a href="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</a>&lt;T&gt;&gt;&nbsp;<a href="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</a>&lt;T&gt;&nbsp;createFieldMatrix(<a href="../../../../../org/apache/commons/math3/Field.html" title="interface in org.apache.commons.math3">Field</a>&lt;T&gt;&nbsp;field,
                                                           int&nbsp;rows,
                                                           int&nbsp;columns)</pre>
<div class="block">Returns a <a href="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear"><code>FieldMatrix</code></a> with specified dimensions.
 <p>The type of matrix returned depends on the dimension. Below
 2<sup>12</sup> elements (i.e. 4096 elements or 64&times;64 for a
 square matrix), a <a href="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear"><code>FieldMatrix</code></a> instance is built. Above
 this threshold a <a href="../../../../../org/apache/commons/math3/linear/BlockFieldMatrix.html" title="class in org.apache.commons.math3.linear"><code>BlockFieldMatrix</code></a> instance is built.</p>
 <p>The matrix elements are all set to field.getZero().</p></div>
<dl><dt><span class="strong">Type Parameters:</span></dt><dd><code>T</code> - the type of the field elements</dd><dt><span class="strong">Parameters:</span></dt><dd><code>field</code> - field to which the matrix elements belong</dd><dd><code>rows</code> - number of rows of the matrix</dd><dd><code>columns</code> - number of columns of the matrix</dd>
<dt><span class="strong">Returns:</span></dt><dd>FieldMatrix with specified dimensions</dd><dt><span class="strong">Since:</span></dt>
  <dd>2.0</dd>
<dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createFieldMatrix(T[][])"><code>createFieldMatrix(FieldElement[][])</code></a></dd></dl>
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<pre>public static&nbsp;<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;createRealMatrix(double[][]&nbsp;data)
                                   throws <a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>,
                                          <a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>,
                                          <a href="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a></pre>
<div class="block">Returns a <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a> whose entries are the the values in the
 the input array.
 <p>The type of matrix returned depends on the dimension. Below
 2<sup>12</sup> elements (i.e. 4096 elements or 64&times;64 for a
 square matrix) which can be stored in a 32kB array, a <a href="../../../../../org/apache/commons/math3/linear/Array2DRowRealMatrix.html" title="class in org.apache.commons.math3.linear"><code>Array2DRowRealMatrix</code></a> instance is built. Above this threshold a <a href="../../../../../org/apache/commons/math3/linear/BlockRealMatrix.html" title="class in org.apache.commons.math3.linear"><code>BlockRealMatrix</code></a> instance is built.</p>
 <p>The input array is copied, not referenced.</p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>data</code> - input array</dd>
<dt><span class="strong">Returns:</span></dt><dd>RealMatrix containing the values of the array</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if <code>data</code> is not rectangular (not all rows have the same length).</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a></code> - if a row or column is empty.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if either <code>data</code> or <code>data[0]</code>
 is <code>null</code>.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if <code>data</code> is not rectangular.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createRealMatrix(int, int)"><code>createRealMatrix(int, int)</code></a></dd></dl>
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<pre>public static&nbsp;&lt;T extends <a href="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</a>&lt;T&gt;&gt;&nbsp;<a href="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</a>&lt;T&gt;&nbsp;createFieldMatrix(T[][]&nbsp;data)
                                                                throws <a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>,
                                                                       <a href="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a>,
                                                                       <a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></pre>
<div class="block">Returns a <a href="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear"><code>FieldMatrix</code></a> whose entries are the the values in the
 the input array.
 <p>The type of matrix returned depends on the dimension. Below
 2<sup>12</sup> elements (i.e. 4096 elements or 64&times;64 for a
 square matrix), a <a href="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear"><code>FieldMatrix</code></a> instance is built. Above
 this threshold a <a href="../../../../../org/apache/commons/math3/linear/BlockFieldMatrix.html" title="class in org.apache.commons.math3.linear"><code>BlockFieldMatrix</code></a> instance is built.</p>
 <p>The input array is copied, not referenced.</p></div>
<dl><dt><span class="strong">Type Parameters:</span></dt><dd><code>T</code> - the type of the field elements</dd><dt><span class="strong">Parameters:</span></dt><dd><code>data</code> - input array</dd>
<dt><span class="strong">Returns:</span></dt><dd>a matrix containing the values of the array.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if <code>data</code> is not rectangular (not all rows have the same length).</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a></code> - if a row or column is empty.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if either <code>data</code> or <code>data[0]</code>
 is <code>null</code>.</dd><dt><span class="strong">Since:</span></dt>
  <dd>2.0</dd>
<dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#createFieldMatrix(org.apache.commons.math3.Field, int, int)"><code>createFieldMatrix(Field, int, int)</code></a></dd></dl>
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<pre>public static&nbsp;<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;createRealIdentityMatrix(int&nbsp;dimension)</pre>
<div class="block">Returns <code>dimension x dimension</code> identity matrix.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>dimension</code> - dimension of identity matrix to generate</dd>
<dt><span class="strong">Returns:</span></dt><dd>identity matrix</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</a></code> - if dimension is not positive</dd><dt><span class="strong">Since:</span></dt>
  <dd>1.1</dd></dl>
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<pre>public static&nbsp;&lt;T extends <a href="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</a>&lt;T&gt;&gt;&nbsp;<a href="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</a>&lt;T&gt;&nbsp;createFieldIdentityMatrix(<a href="../../../../../org/apache/commons/math3/Field.html" title="interface in org.apache.commons.math3">Field</a>&lt;T&gt;&nbsp;field,
                                                                   int&nbsp;dimension)</pre>
<div class="block">Returns <code>dimension x dimension</code> identity matrix.</div>
<dl><dt><span class="strong">Type Parameters:</span></dt><dd><code>T</code> - the type of the field elements</dd><dt><span class="strong">Parameters:</span></dt><dd><code>field</code> - field to which the elements belong</dd><dd><code>dimension</code> - dimension of identity matrix to generate</dd>
<dt><span class="strong">Returns:</span></dt><dd>identity matrix</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</a></code> - if dimension is not positive</dd><dt><span class="strong">Since:</span></dt>
  <dd>2.0</dd></dl>
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<pre>public static&nbsp;<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;createRealDiagonalMatrix(double[]&nbsp;diagonal)</pre>
<div class="block">Returns a diagonal matrix with specified elements.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>diagonal</code> - diagonal elements of the matrix (the array elements
 will be copied)</dd>
<dt><span class="strong">Returns:</span></dt><dd>diagonal matrix</dd><dt><span class="strong">Since:</span></dt>
  <dd>2.0</dd></dl>
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<pre>public static&nbsp;&lt;T extends <a href="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</a>&lt;T&gt;&gt;&nbsp;<a href="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</a>&lt;T&gt;&nbsp;createFieldDiagonalMatrix(T[]&nbsp;diagonal)</pre>
<div class="block">Returns a diagonal matrix with specified elements.</div>
<dl><dt><span class="strong">Type Parameters:</span></dt><dd><code>T</code> - the type of the field elements</dd><dt><span class="strong">Parameters:</span></dt><dd><code>diagonal</code> - diagonal elements of the matrix (the array elements
 will be copied)</dd>
<dt><span class="strong">Returns:</span></dt><dd>diagonal matrix</dd><dt><span class="strong">Since:</span></dt>
  <dd>2.0</dd></dl>
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                                   throws <a href="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a>,
                                          <a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></pre>
<div class="block">Creates a <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear"><code>RealVector</code></a> using the data from the input array.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>data</code> - the input data</dd>
<dt><span class="strong">Returns:</span></dt><dd>a data.length RealVector</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a></code> - if <code>data</code> is empty.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if <code>data</code> is <code>null</code>.</dd></dl>
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                                                                throws <a href="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a>,
                                                                       <a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>,
                                                                       <a href="../../../../../org/apache/commons/math3/exception/ZeroException.html" title="class in org.apache.commons.math3.exception">ZeroException</a></pre>
<div class="block">Creates a <a href="../../../../../org/apache/commons/math3/linear/FieldVector.html" title="interface in org.apache.commons.math3.linear"><code>FieldVector</code></a> using the data from the input array.</div>
<dl><dt><span class="strong">Type Parameters:</span></dt><dd><code>T</code> - the type of the field elements</dd><dt><span class="strong">Parameters:</span></dt><dd><code>data</code> - the input data</dd>
<dt><span class="strong">Returns:</span></dt><dd>a data.length FieldVector</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a></code> - if <code>data</code> is empty.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if <code>data</code> is <code>null</code>.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/ZeroException.html" title="class in org.apache.commons.math3.exception">ZeroException</a></code> - if <code>data</code> has 0 elements</dd></dl>
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                                      throws <a href="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a>,
                                             <a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></pre>
<div class="block">Create a row <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a> using the data from the input
 array.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>rowData</code> - the input row data</dd>
<dt><span class="strong">Returns:</span></dt><dd>a 1 x rowData.length RealMatrix</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a></code> - if <code>rowData</code> is empty.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if <code>rowData</code> is <code>null</code>.</dd></dl>
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                                                                   throws <a href="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a>,
                                                                          <a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></pre>
<div class="block">Create a row <a href="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear"><code>FieldMatrix</code></a> using the data from the input
 array.</div>
<dl><dt><span class="strong">Type Parameters:</span></dt><dd><code>T</code> - the type of the field elements</dd><dt><span class="strong">Parameters:</span></dt><dd><code>rowData</code> - the input row data</dd>
<dt><span class="strong">Returns:</span></dt><dd>a 1 x rowData.length FieldMatrix</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a></code> - if <code>rowData</code> is empty.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if <code>rowData</code> is <code>null</code>.</dd></dl>
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<pre>public static&nbsp;<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;createColumnRealMatrix(double[]&nbsp;columnData)
                                         throws <a href="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a>,
                                                <a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></pre>
<div class="block">Creates a column <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a> using the data from the input
 array.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>columnData</code> - the input column data</dd>
<dt><span class="strong">Returns:</span></dt><dd>a columnData x 1 RealMatrix</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a></code> - if <code>columnData</code> is empty.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if <code>columnData</code> is <code>null</code>.</dd></dl>
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<pre>public static&nbsp;&lt;T extends <a href="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</a>&lt;T&gt;&gt;&nbsp;<a href="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</a>&lt;T&gt;&nbsp;createColumnFieldMatrix(T[]&nbsp;columnData)
                                                                      throws <a href="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a>,
                                                                             <a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></pre>
<div class="block">Creates a column <a href="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear"><code>FieldMatrix</code></a> using the data from the input
 array.</div>
<dl><dt><span class="strong">Type Parameters:</span></dt><dd><code>T</code> - the type of the field elements</dd><dt><span class="strong">Parameters:</span></dt><dd><code>columnData</code> - the input column data</dd>
<dt><span class="strong">Returns:</span></dt><dd>a columnData x 1 FieldMatrix</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a></code> - if <code>data</code> is empty.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if <code>columnData</code> is <code>null</code>.</dd></dl>
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<pre>public static&nbsp;void&nbsp;checkSymmetric(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;matrix,
                  double&nbsp;eps)</pre>
<div class="block">Checks whether a matrix is symmetric.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>matrix</code> - Matrix to check.</dd><dd><code>eps</code> - Relative tolerance.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math3.linear">NonSquareMatrixException</a></code> - if the matrix is not square.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSymmetricMatrixException.html" title="class in org.apache.commons.math3.linear">NonSymmetricMatrixException</a></code> - if the matrix is not symmetric.</dd><dt><span class="strong">Since:</span></dt>
  <dd>3.1</dd></dl>
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<pre>public static&nbsp;boolean&nbsp;isSymmetric(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;matrix,
                  double&nbsp;eps)</pre>
<div class="block">Checks whether a matrix is symmetric.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>matrix</code> - Matrix to check.</dd><dd><code>eps</code> - Relative tolerance.</dd>
<dt><span class="strong">Returns:</span></dt><dd><code>true</code> if <code>matrix</code> is symmetric.</dd><dt><span class="strong">Since:</span></dt>
  <dd>3.1</dd></dl>
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<pre>public static&nbsp;void&nbsp;checkMatrixIndex(<a href="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</a>&nbsp;m,
                    int&nbsp;row,
                    int&nbsp;column)
                             throws <a href="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</a></pre>
<div class="block">Check if matrix indices are valid.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>m</code> - Matrix.</dd><dd><code>row</code> - Row index to check.</dd><dd><code>column</code> - Column index to check.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</a></code> - if <code>row</code> or <code>column</code> is not
 a valid index.</dd></dl>
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<pre>public static&nbsp;void&nbsp;checkRowIndex(<a href="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</a>&nbsp;m,
                 int&nbsp;row)
                          throws <a href="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</a></pre>
<div class="block">Check if a row index is valid.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>m</code> - Matrix.</dd><dd><code>row</code> - Row index to check.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</a></code> - if <code>row</code> is not a valid index.</dd></dl>
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<pre>public static&nbsp;void&nbsp;checkColumnIndex(<a href="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</a>&nbsp;m,
                    int&nbsp;column)
                             throws <a href="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</a></pre>
<div class="block">Check if a column index is valid.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>m</code> - Matrix.</dd><dd><code>column</code> - Column index to check.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</a></code> - if <code>column</code> is not a valid index.</dd></dl>
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<pre>public static&nbsp;void&nbsp;checkSubMatrixIndex(<a href="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</a>&nbsp;m,
                       int&nbsp;startRow,
                       int&nbsp;endRow,
                       int&nbsp;startColumn,
                       int&nbsp;endColumn)
                                throws <a href="../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</a>,
                                       <a href="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</a></pre>
<div class="block">Check if submatrix ranges indices are valid.
 Rows and columns are indicated counting from 0 to <code>n - 1</code>.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>m</code> - Matrix.</dd><dd><code>startRow</code> - Initial row index.</dd><dd><code>endRow</code> - Final row index.</dd><dd><code>startColumn</code> - Initial column index.</dd><dd><code>endColumn</code> - Final column index.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</a></code> - if the indices are invalid.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</a></code> - if <code>endRow &lt; startRow</code> or
 <code>endColumn &lt; startColumn</code>.</dd></dl>
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<pre>public static&nbsp;void&nbsp;checkSubMatrixIndex(<a href="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</a>&nbsp;m,
                       int[]&nbsp;selectedRows,
                       int[]&nbsp;selectedColumns)
                                throws <a href="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a>,
                                       <a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>,
                                       <a href="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</a></pre>
<div class="block">Check if submatrix ranges indices are valid.
 Rows and columns are indicated counting from 0 to n-1.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>m</code> - Matrix.</dd><dd><code>selectedRows</code> - Array of row indices.</dd><dd><code>selectedColumns</code> - Array of column indices.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if <code>selectedRows</code> or
 <code>selectedColumns</code> are <code>null</code>.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a></code> - if the row or column selections are empty (zero
 length).</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</a></code> - if row or column selections are not valid.</dd></dl>
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<pre>public static&nbsp;void&nbsp;checkAdditionCompatible(<a href="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</a>&nbsp;left,
                           <a href="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</a>&nbsp;right)
                                    throws <a href="../../../../../org/apache/commons/math3/linear/MatrixDimensionMismatchException.html" title="class in org.apache.commons.math3.linear">MatrixDimensionMismatchException</a></pre>
<div class="block">Check if matrices are addition compatible.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>left</code> - Left hand side matrix.</dd><dd><code>right</code> - Right hand side matrix.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/MatrixDimensionMismatchException.html" title="class in org.apache.commons.math3.linear">MatrixDimensionMismatchException</a></code> - if the matrices are not addition
 compatible.</dd></dl>
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<pre>public static&nbsp;void&nbsp;checkSubtractionCompatible(<a href="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</a>&nbsp;left,
                              <a href="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</a>&nbsp;right)
                                       throws <a href="../../../../../org/apache/commons/math3/linear/MatrixDimensionMismatchException.html" title="class in org.apache.commons.math3.linear">MatrixDimensionMismatchException</a></pre>
<div class="block">Check if matrices are subtraction compatible</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>left</code> - Left hand side matrix.</dd><dd><code>right</code> - Right hand side matrix.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/MatrixDimensionMismatchException.html" title="class in org.apache.commons.math3.linear">MatrixDimensionMismatchException</a></code> - if the matrices are not addition
 compatible.</dd></dl>
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<pre>public static&nbsp;void&nbsp;checkMultiplicationCompatible(<a href="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</a>&nbsp;left,
                                 <a href="../../../../../org/apache/commons/math3/linear/AnyMatrix.html" title="interface in org.apache.commons.math3.linear">AnyMatrix</a>&nbsp;right)
                                          throws <a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></pre>
<div class="block">Check if matrices are multiplication compatible</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>left</code> - Left hand side matrix.</dd><dd><code>right</code> - Right hand side matrix.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if matrices are not multiplication
 compatible.</dd></dl>
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<h4>fractionMatrixToRealMatrix</h4>
<pre>public static&nbsp;<a href="../../../../../org/apache/commons/math3/linear/Array2DRowRealMatrix.html" title="class in org.apache.commons.math3.linear">Array2DRowRealMatrix</a>&nbsp;fractionMatrixToRealMatrix(<a href="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</a>&lt;<a href="../../../../../org/apache/commons/math3/fraction/Fraction.html" title="class in org.apache.commons.math3.fraction">Fraction</a>&gt;&nbsp;m)</pre>
<div class="block">Convert a <a href="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear"><code>FieldMatrix</code></a>/<a href="../../../../../org/apache/commons/math3/fraction/Fraction.html" title="class in org.apache.commons.math3.fraction"><code>Fraction</code></a> matrix to a <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a>.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>m</code> - Matrix to convert.</dd>
<dt><span class="strong">Returns:</span></dt><dd>the converted matrix.</dd></dl>
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<pre>public static&nbsp;<a href="../../../../../org/apache/commons/math3/linear/Array2DRowRealMatrix.html" title="class in org.apache.commons.math3.linear">Array2DRowRealMatrix</a>&nbsp;bigFractionMatrixToRealMatrix(<a href="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</a>&lt;<a href="../../../../../org/apache/commons/math3/fraction/BigFraction.html" title="class in org.apache.commons.math3.fraction">BigFraction</a>&gt;&nbsp;m)</pre>
<div class="block">Convert a <a href="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear"><code>FieldMatrix</code></a>/<a href="../../../../../org/apache/commons/math3/fraction/BigFraction.html" title="class in org.apache.commons.math3.fraction"><code>BigFraction</code></a> matrix to a <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a>.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>m</code> - Matrix to convert.</dd>
<dt><span class="strong">Returns:</span></dt><dd>the converted matrix.</dd></dl>
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<pre>public static&nbsp;void&nbsp;serializeRealVector(<a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a>&nbsp;vector,
                       <a href="http://docs.oracle.com/javase/6/docs/api/java/io/ObjectOutputStream.html?is-external=true" title="class or interface in java.io">ObjectOutputStream</a>&nbsp;oos)
                                throws <a href="http://docs.oracle.com/javase/6/docs/api/java/io/IOException.html?is-external=true" title="class or interface in java.io">IOException</a></pre>
<div class="block">Serialize a <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear"><code>RealVector</code></a>.
 <p>
 This method is intended to be called from within a private
 <code>writeObject</code> method (after a call to
 <code>oos.defaultWriteObject()</code>) in a class that has a
 <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear"><code>RealVector</code></a> field, which should be declared <code>transient</code>.
 This way, the default handling does not serialize the vector (the <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear"><code>RealVector</code></a> interface is not serializable by default) but this method does
 serialize it specifically.
 </p>
 <p>
 The following example shows how a simple class with a name and a real vector
 should be written:
 <pre><code>
 public class NamedVector implements Serializable {

     private final String name;
     private final transient RealVector coefficients;

     // omitted constructors, getters ...

     private void writeObject(ObjectOutputStream oos) throws IOException {
         oos.defaultWriteObject();  // takes care of name field
         MatrixUtils.serializeRealVector(coefficients, oos);
     }

     private void readObject(ObjectInputStream ois) throws ClassNotFoundException, IOException {
         ois.defaultReadObject();  // takes care of name field
         MatrixUtils.deserializeRealVector(this, "coefficients", ois);
     }

 }
 </code></pre>
 </p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>vector</code> - real vector to serialize</dd><dd><code>oos</code> - stream where the real vector should be written</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="http://docs.oracle.com/javase/6/docs/api/java/io/IOException.html?is-external=true" title="class or interface in java.io">IOException</a></code> - if object cannot be written to stream</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#deserializeRealVector(java.lang.Object, java.lang.String, java.io.ObjectInputStream)"><code>deserializeRealVector(Object, String, ObjectInputStream)</code></a></dd></dl>
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<pre>public static&nbsp;void&nbsp;deserializeRealVector(<a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a>&nbsp;instance,
                         <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</a>&nbsp;fieldName,
                         <a href="http://docs.oracle.com/javase/6/docs/api/java/io/ObjectInputStream.html?is-external=true" title="class or interface in java.io">ObjectInputStream</a>&nbsp;ois)
                                  throws <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/ClassNotFoundException.html?is-external=true" title="class or interface in java.lang">ClassNotFoundException</a>,
                                         <a href="http://docs.oracle.com/javase/6/docs/api/java/io/IOException.html?is-external=true" title="class or interface in java.io">IOException</a></pre>
<div class="block">Deserialize  a <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear"><code>RealVector</code></a> field in a class.
 <p>
 This method is intended to be called from within a private
 <code>readObject</code> method (after a call to
 <code>ois.defaultReadObject()</code>) in a class that has a
 <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear"><code>RealVector</code></a> field, which should be declared <code>transient</code>.
 This way, the default handling does not deserialize the vector (the <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear"><code>RealVector</code></a> interface is not serializable by default) but this method does
 deserialize it specifically.
 </p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>instance</code> - instance in which the field must be set up</dd><dd><code>fieldName</code> - name of the field within the class (may be private and final)</dd><dd><code>ois</code> - stream from which the real vector should be read</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/ClassNotFoundException.html?is-external=true" title="class or interface in java.lang">ClassNotFoundException</a></code> - if a class in the stream cannot be found</dd>
<dd><code><a href="http://docs.oracle.com/javase/6/docs/api/java/io/IOException.html?is-external=true" title="class or interface in java.io">IOException</a></code> - if object cannot be read from the stream</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#serializeRealVector(org.apache.commons.math3.linear.RealVector, java.io.ObjectOutputStream)"><code>serializeRealVector(RealVector, ObjectOutputStream)</code></a></dd></dl>
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<pre>public static&nbsp;void&nbsp;serializeRealMatrix(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;matrix,
                       <a href="http://docs.oracle.com/javase/6/docs/api/java/io/ObjectOutputStream.html?is-external=true" title="class or interface in java.io">ObjectOutputStream</a>&nbsp;oos)
                                throws <a href="http://docs.oracle.com/javase/6/docs/api/java/io/IOException.html?is-external=true" title="class or interface in java.io">IOException</a></pre>
<div class="block">Serialize a <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a>.
 <p>
 This method is intended to be called from within a private
 <code>writeObject</code> method (after a call to
 <code>oos.defaultWriteObject()</code>) in a class that has a
 <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a> field, which should be declared <code>transient</code>.
 This way, the default handling does not serialize the matrix (the <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a> interface is not serializable by default) but this method does
 serialize it specifically.
 </p>
 <p>
 The following example shows how a simple class with a name and a real matrix
 should be written:
 <pre><code>
 public class NamedMatrix implements Serializable {

     private final String name;
     private final transient RealMatrix coefficients;

     // omitted constructors, getters ...

     private void writeObject(ObjectOutputStream oos) throws IOException {
         oos.defaultWriteObject();  // takes care of name field
         MatrixUtils.serializeRealMatrix(coefficients, oos);
     }

     private void readObject(ObjectInputStream ois) throws ClassNotFoundException, IOException {
         ois.defaultReadObject();  // takes care of name field
         MatrixUtils.deserializeRealMatrix(this, "coefficients", ois);
     }

 }
 </code></pre>
 </p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>matrix</code> - real matrix to serialize</dd><dd><code>oos</code> - stream where the real matrix should be written</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="http://docs.oracle.com/javase/6/docs/api/java/io/IOException.html?is-external=true" title="class or interface in java.io">IOException</a></code> - if object cannot be written to stream</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#deserializeRealMatrix(java.lang.Object, java.lang.String, java.io.ObjectInputStream)"><code>deserializeRealMatrix(Object, String, ObjectInputStream)</code></a></dd></dl>
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<pre>public static&nbsp;void&nbsp;deserializeRealMatrix(<a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a>&nbsp;instance,
                         <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</a>&nbsp;fieldName,
                         <a href="http://docs.oracle.com/javase/6/docs/api/java/io/ObjectInputStream.html?is-external=true" title="class or interface in java.io">ObjectInputStream</a>&nbsp;ois)
                                  throws <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/ClassNotFoundException.html?is-external=true" title="class or interface in java.lang">ClassNotFoundException</a>,
                                         <a href="http://docs.oracle.com/javase/6/docs/api/java/io/IOException.html?is-external=true" title="class or interface in java.io">IOException</a></pre>
<div class="block">Deserialize  a <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a> field in a class.
 <p>
 This method is intended to be called from within a private
 <code>readObject</code> method (after a call to
 <code>ois.defaultReadObject()</code>) in a class that has a
 <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a> field, which should be declared <code>transient</code>.
 This way, the default handling does not deserialize the matrix (the <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a> interface is not serializable by default) but this method does
 deserialize it specifically.
 </p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>instance</code> - instance in which the field must be set up</dd><dd><code>fieldName</code> - name of the field within the class (may be private and final)</dd><dd><code>ois</code> - stream from which the real matrix should be read</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/ClassNotFoundException.html?is-external=true" title="class or interface in java.lang">ClassNotFoundException</a></code> - if a class in the stream cannot be found</dd>
<dd><code><a href="http://docs.oracle.com/javase/6/docs/api/java/io/IOException.html?is-external=true" title="class or interface in java.io">IOException</a></code> - if object cannot be read from the stream</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#serializeRealMatrix(org.apache.commons.math3.linear.RealMatrix, java.io.ObjectOutputStream)"><code>serializeRealMatrix(RealMatrix, ObjectOutputStream)</code></a></dd></dl>
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<pre>public static&nbsp;void&nbsp;solveLowerTriangularSystem(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;rm,
                              <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a>&nbsp;b)
                                       throws <a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>,
                                              <a href="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a>,
                                              <a href="../../../../../org/apache/commons/math3/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math3.linear">NonSquareMatrixException</a></pre>
<div class="block">Solve  a  system of composed of a Lower Triangular Matrix
 <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a>.
 <p>
 This method is called to solve systems of equations which are
 of the lower triangular form. The matrix <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a>
 is assumed, though not checked, to be in lower triangular form.
 The vector <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear"><code>RealVector</code></a> is overwritten with the solution.
 The matrix is checked that it is square and its dimensions match
 the length of the vector.
 </p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>rm</code> - RealMatrix which is lower triangular</dd><dd><code>b</code> - RealVector this is overwritten</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the matrix and vector are not
 conformable</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math3.linear">NonSquareMatrixException</a></code> - if the matrix <code>rm</code> is not square</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></code> - if the absolute value of one of the diagonal
 coefficient of <code>rm</code> is lower than <a href="../../../../../org/apache/commons/math3/util/Precision.html#SAFE_MIN"><code>Precision.SAFE_MIN</code></a></dd></dl>
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<pre>public static&nbsp;void&nbsp;solveUpperTriangularSystem(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;rm,
                              <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a>&nbsp;b)
                                       throws <a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>,
                                              <a href="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a>,
                                              <a href="../../../../../org/apache/commons/math3/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math3.linear">NonSquareMatrixException</a></pre>
<div class="block">Solver a  system composed  of an Upper Triangular Matrix
 <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a>.
 <p>
 This method is called to solve systems of equations which are
 of the lower triangular form. The matrix <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear"><code>RealMatrix</code></a>
 is assumed, though not checked, to be in upper triangular form.
 The vector <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear"><code>RealVector</code></a> is overwritten with the solution.
 The matrix is checked that it is square and its dimensions match
 the length of the vector.
 </p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>rm</code> - RealMatrix which is upper triangular</dd><dd><code>b</code> - RealVector this is overwritten</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the matrix and vector are not
 conformable</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math3.linear">NonSquareMatrixException</a></code> - if the matrix <code>rm</code> is not
 square</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></code> - if the absolute value of one of the diagonal
 coefficient of <code>rm</code> is lower than <a href="../../../../../org/apache/commons/math3/util/Precision.html#SAFE_MIN"><code>Precision.SAFE_MIN</code></a></dd></dl>
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<pre>public static&nbsp;<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;blockInverse(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;m,
                      int&nbsp;splitIndex)</pre>
<div class="block">Computes the inverse of the given matrix by splitting it into
 4 sub-matrices.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>m</code> - Matrix whose inverse must be computed.</dd><dd><code>splitIndex</code> - Index that determines the "split" line and
 column.
 The element corresponding to this index will part of the
 upper-left sub-matrix.</dd>
<dt><span class="strong">Returns:</span></dt><dd>the inverse of <code>m</code>.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math3.linear">NonSquareMatrixException</a></code> - if <code>m</code> is not square.</dd></dl>
</li>
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<h4>inverse</h4>
<pre>public static&nbsp;<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;inverse(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;matrix)
                          throws <a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>,
                                 <a href="../../../../../org/apache/commons/math3/linear/SingularMatrixException.html" title="class in org.apache.commons.math3.linear">SingularMatrixException</a>,
                                 <a href="../../../../../org/apache/commons/math3/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math3.linear">NonSquareMatrixException</a></pre>
<div class="block">Computes the inverse of the given matrix.
 <p>
 By default, the inverse of the matrix is computed using the QR-decomposition,
 unless a more efficient method can be determined for the input matrix.
 <p>
 Note: this method will use a singularity threshold of 0,
 use <a href="../../../../../org/apache/commons/math3/linear/MatrixUtils.html#inverse(org.apache.commons.math3.linear.RealMatrix, double)"><code>inverse(RealMatrix, double)</code></a> if a different threshold is needed.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>matrix</code> - Matrix whose inverse shall be computed</dd>
<dt><span class="strong">Returns:</span></dt><dd>the inverse of <code>matrix</code></dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if <code>matrix</code> is <code>null</code></dd>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/SingularMatrixException.html" title="class in org.apache.commons.math3.linear">SingularMatrixException</a></code> - if m is singular</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math3.linear">NonSquareMatrixException</a></code> - if matrix is not square</dd><dt><span class="strong">Since:</span></dt>
  <dd>3.3</dd></dl>
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<h4>inverse</h4>
<pre>public static&nbsp;<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;inverse(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;matrix,
                 double&nbsp;threshold)
                          throws <a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>,
                                 <a href="../../../../../org/apache/commons/math3/linear/SingularMatrixException.html" title="class in org.apache.commons.math3.linear">SingularMatrixException</a>,
                                 <a href="../../../../../org/apache/commons/math3/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math3.linear">NonSquareMatrixException</a></pre>
<div class="block">Computes the inverse of the given matrix.
 <p>
 By default, the inverse of the matrix is computed using the QR-decomposition,
 unless a more efficient method can be determined for the input matrix.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>matrix</code> - Matrix whose inverse shall be computed</dd><dd><code>threshold</code> - Singularity threshold</dd>
<dt><span class="strong">Returns:</span></dt><dd>the inverse of <code>m</code></dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if <code>matrix</code> is <code>null</code></dd>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/SingularMatrixException.html" title="class in org.apache.commons.math3.linear">SingularMatrixException</a></code> - if matrix is singular</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math3.linear">NonSquareMatrixException</a></code> - if matrix is not square</dd><dt><span class="strong">Since:</span></dt>
  <dd>3.3</dd></dl>
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